Alternatively, you could reach out to a mortgage broker and have them get you prequalified so that you can prove that you can afford the house.

Im happy to share any info I have based on my personal expierences along with my referl network.

I would like to find a lender who can approve me based on the property and what it will bring in monthly as a rental rather than on my personal finance and credit. 

You are obligated to provide the oldest verifiable operating statement (base year), which is adjusted into today's dollars (Using an LA City formula for inflation) and this is compared to your current year (yes with receipts, cancelled checks, bank statements, k1's etc), which can be significant. 

A 1031 exchange can be a good option because although there is no cash involved in the deal, you would still recognize a gain based on the fair market value of the properties being received over the basis of the property you're giving up (if it's a gain).

This will help guide you to the best cities based on your expectations.

Your loan amount will be based on the lower of the purchase price and appraised value. 

I am based in Charlottesville VA and even though I make excellent cash flow on my STRs, that cash flow has always been dwarfed by my appreciation.

This amount is not refundable and would be based on good credit (% would increase for credit below 730).

So lets say the property is valued at 200,000 could a brand new LLC borrow 150,000 to 160,000 to purchase an investment property where the rent would be 1400 to 1500/month.Or since I own the LLC is it strictly based on my ability to get financed?